What is the minimum number of students, Mathematics

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Question 1:

What is the minimum number of students each of whom comes from one of the 50 different states, enrolled in a university to guarantee that there are at least 100 who come from the same state?

Question 2:

Show that there are 45 bit strings that contain exactly eight 0s and ten 1s if every 0 must be immediately followed by a 1.


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